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@ARTICLE{Rost:1005325,
      author       = {Rost, Stefan and Blügel, Stefan and Friedrich, Christoph},
      title        = {{E}fficient calculation of k -integrated electron energy
                      loss spectra: {A}pplication to monolayers of {M}o{S} 2 ,  
                      h{BN} , and graphene},
      journal      = {Physical review / B},
      volume       = {107},
      number       = {8},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2023-01434},
      pages        = {085132},
      year         = {2023},
      abstract     = {The theoretical scattering cross section of electron energy
                      loss spectroscopy (EELS) is essentially given by
                      $-\text{Im}\,\varepsilon^{-1}(\mathbf{k},\omega)$ with the
                      energy loss $\hbar\omega$ and the momentum transfer
                      $\hbar\mathbf{k}$. The macroscopic dielectric function
                      $\varepsilon(\mathbf{k},\omega)$ can be calculated from
                      first principles using time-dependent density-functional
                      theory.However, experimental EELS measurements have a finite
                      $\mathbf{k}$ resolution or, when operated in spatial
                      resolution mode, yield a $\mathbf{k}$-integrated loss
                      spectrum, which deviates significantly from EEL spectra
                      calculated for specific $\mathbf{k}$ momenta. On the other
                      hand, integrating the theoretical spectra over $\mathbf{k}$
                      is complicated by the fact that the integrand varies over
                      several (typically six) orders of magnitude around $k=0$.In
                      this article, we present a stable technique for integrating
                      EEL spectra over an adjustable range of momentum transfers.
                      The important region around $k=0$, where the integrand is
                      nearly divergent, is treated partially analytically,
                      allowing an analytic integration of the near-divergence. The
                      scheme is applied to three prototypical two-dimensional
                      systems: monolayers of MoS$_2$ (semiconductor), hexagonal BN
                      (insulator), and graphene (semimetal).Here, we are
                      confronted with the added difficulty that the long-range
                      Coulomb interaction leads to a very slow supercell (vacuum
                      size) convergence. We address this difficulty by employing
                      an extrapolation scheme, enabling an efficient reduction of
                      the supercell size and thus a considerable speed-up in
                      computation time. The calculated $\mathbf{k}$-integrated
                      spectra are in very favourable agreement with experimental
                      EEL spectra.},
      cin          = {PGI-1},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-1-20110106},
      pnm          = {5211 - Topological Matter (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5211},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000944014500003},
      doi          = {10.1103/PhysRevB.107.085132},
      url          = {https://juser.fz-juelich.de/record/1005325},
}